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Local structure of groups and of their classifying spaces

Introductory Workshop: Algebraic Topology January 27, 2014 - January 31, 2014

January 30, 2014 (09:30 AM PST - 10:30 AM PST)
Speaker(s): Bob Oliver (Université de Paris XIII (Paris-Nord))
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC



This will be a survey talk on the close relationship between the local structure of a nite group or compact Lie group and that of its classifying space. By the p-local structure of a group G, for a prime p, is meant the structure of a Sylow p-subgroup S  G (a maximal p-toral subgroup if G is compact Lie), together with all G-conjugacy relations between elements and subgroups of S. By the p-local structure of the classifying space BG is meant the structure (homotopy properties) of its p-completion BG^p . For example, by a conjecture of Martino and Priddy, now a theorem, two nite groups G and H have equivalent p-local structures if and only if BG^p ' BH^p . This was used, in joint work with Broto and Møller, to prove a general theorem about local equivalences between nite Lie groups  a result for which no purely algebraic proof is known. As another example, these ideas have allowed us to extend the family of p-completed classifying spaces of (nite or compact Lie) groups to a much larger family of spaces which have many of the same very nice homotopy theoretic properties.

19458?type=thumb Local structure of groups and of their classifying spaces 55.6 KB application/pdf Download
20106?type=thumb Oliver notes 6.22 MB application/pdf Download
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